On the Accuracy of an Elliptical Orbit Determination
The present paper concerns the problem of determining the variations in the six orbital elements of a planetary body when one or more of the original observations are affected by known errors. Differential expressions are derived for these variations which eliminate the necessity of having to re-compute the orbit several times. A numerical example is included in which results of these expressions are compared with actual residuals as obtained from two orbital calculations of the same asteroid.
KeywordsOrbital Element Earth Satellite Naval Research Laboratory Planetary Orbit Planetary Body
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- Heinrich K. Eichhorn,Mitteilungen der Universitäts-Sternwarte Wien, 5, 169–184 (1952).Google Scholar
- In the case of the earth satellite, the observer is moving along a circle of latitude whose plane, unlike that of the satellite orbit, does not, necessarily, pass through the geocenter; whereas in the other case, both earth and planet are moving in Keplerian ellipses.Google Scholar
- Heinrich K. Eichhorn,Mitteilungen der Universitäts-Sternwarte Wien, 4, 149–171 (1950).Google Scholar
- Since a, e,and t o are related to the eccentric anomaly, E,by a transcendental equation, we follow the suggestion of Eichhorn and avoid considerable complication by first solving for the three eccentric anomalies corresponding to the three observation times, and then computing the changes in a, e,and t o from these intermediary elements.Google Scholar
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- The choice as to whether or not these simplifications should be included will, of course, depend entirely on the accuracy required of each particular application of this problem.Google Scholar
- Kenneth P. Williams,The Calculation of the Orbits of Asteroids and Comets, The Principia Press, Inc., 153–167 (1934).Google Scholar
- This system obtains the angular position of a radio source by measuring the difference in the radio path lengths from the source to each of two antennas. This difference is determined by means of a phase difference between the signal received at the antennas and at the receiver output.Google Scholar